The finding prompted shock and outrage across the country.
The bag in which the infant was dumped was being carried the dog when a passer-by heard the baby crying, local media said.
The baby was taken to the Islamic Hospital by the unidentified bystander, and later transferred to the Tripoli Government Hospital.
Images on social media show the baby, who appears to be about four months old, with bruises on her face and body.
Condemnation over her abandonment was swift as the news spread, and offers to adopt the baby poured in through social media.
“Some say that the dog is an unclean animal and, of course, this is not true," one commentator, Farid, said on Twitter.
"The dog has much more humanity, kindness, cunning and intelligence than some satanic mutants in human form."
Another tweeted: “Animals have more compassion than humans."
The National tried to contact the municipality of Tripoli, where the baby was abandoned, and the Tripoli Government Hospital where she is being treated, but did not receive a reply.
Wednesday is the start of the Islamic New Year, a national holiday, so public institutions are closed.
Several instances of child abuse have come to light in Lebanon in recent weeks.
Last week, a nursery employee was arrested and the institution permanently closed after videos appeared of the employee allegedly mistreating infants.
And in early July, Lynn Talib, 6, died in the northern region of Miniyeh. Medical forensic reports later revealed she had been sexually assaulted before her death.
Experts say it is impossible to know whether cases of child abuse are on the increase because there is no central system for monitoring statistics, given the financial difficulties facing state institutions.
But anecdotal instances of child dumping and abuse have increased as the country slides further into destitution.
Tripoli, Lebanon’s second-largest city, has the highest poverty rate in a country where about 80 per cent of the population is poor as a result of an economic crisis that began in 2019.